Warp-power-scaling data point

As some of you know from the "Let's talk about the Romulan BOP" thread, I've been working on calculations for theoretical power outputs of different fusion reactions of different fusion fuels.

The first thing I found, and I won't spend as much time on this as I could, is that deuterium (heavy hydrogen) is a far superior fuel in almost every way to protium (light hydrogen). Deuterium has five reactions to choose from and they delineate well from relatively easy to near impossible. Protium only has three and the easiest is very difficult and complicated. (The hardest protium reaction is equally near impossible as the hardest deuterium reaction.) Under the same tankage deuterium has twice the density of protium and since fusion energy is all about the change in mass from fuel to exhaust, this is important.

There are two drawbacks to deuterium:
1) Biology incorporates protium. Deuterated chemicals do not react quite the same and though they are not quite poisonous, neither are they useful. IE, drink enough heavy water and you will die because your chemical biology will not be able to incorporate the slightly different chemestry of deuterium. If you were to use protium as your fuel then you could store some of your fuel in your food and water, allowing for a larger tankage without increasing your fuel tanks. This is not possible with deuterium, as such....Of course, replicators would change this equation somewhat.

2) The main of the interstellar medium is protium. The ability to augment your fuel supply by scooping up the interstellar medium while in flight would mean an increased range. Indeed, if enough could be scooped up, you could have a nearly infinite range. (I argued this in the above Romulan BOP thread.) Again, replicators or anti-xeno-effect chambers could negate this disadvantage.

Ok. But this is not what I came her to write about.

It is perfectly possible to store your fusion fuel --deuterium-- in a chemical compound in order to either greatly decrease the size of the tankage or to greatly increase the energy density per volume. Not only that, but by storing it in a chemical that is easier to store --less cryogenic, for example-- you also greatly decrease the mass of the tanks. However, in doing so you will decrease the energy density per kilogram of the fuel. This is an engineering trade off that is quite familiar in cars and airplanes: hydrogen has much more chemical energy per kilogram than gasoline, but is harder to store and has far less energy per liter. In cars and airplanes, the advantages of having a small, simple tank outweigh the disadvantage of lugging around more mass for the same energy output.

Since it's reasonable to assume Star Fleet engineers could easily realize the possibility of chemical storage of deuterium but choose to store it as a liquid instead, it seems to me, for some technical reason, energy density per kilogram is more important than energy density per liter.

Theoretically, this is true for rocket propulsion, which is what I usually assume impulse engines to be: With the same wet-to-dry mass ratio, liquid deuterium has more delta_V (change in velocity) than any of the hydrocarbons I've studied. However, practically speaking, ease of tankage and better per-volume density translates into a higher wet-to-dry mass ratio, making deuterated propane a higher performing fuel for rocket propulsion even with its considerably lower mass-to-enegy conversion. (I can back up these statements with theoretical calculations.)

This leaves warp drive as the primary reason to use liquid deuterium. I deduce from these observations that, every thing else being equal, pushing around more mass is a heavier burden than making a larger warp field. IE, warp power requirements scale more quickly with increased mass than with increased volume.

Let me say that again. I deduce from fusion fuel storage methodology that: Power requirements for warp fields increase more quickly with increased mass than with increased volume.

Deuterated chemicals do not react quite the same and though they are not quite poisonous, neither are they useful. IE, drink enough heavy water and you will die because your chemical biology will not be able to incorporate the slightly different chemestry of deuterium.

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This always reminds me of the scene in the original "V-The Visitors" where the main protagonist goes to these huge tanks aboard the V-saucer and opens a valve to taste it. Last time I thought "What is the idiot doing, drinking deuterium?" but of course it just turned out to be water...doh!

I had been under the impression (like in "Oblivion") that aliens would harvest deuterium from our sea water but those in "V" apparently could cross vast interstellar distances but didn't have a fracking clue how to manufacture H20... (IIRC we had one Star Trek species with the same "capabilities" but I'll leave it to someone else to name it - Seriously, turned me off at first to continue watching this ST series).

It is perfectly possible to store your fusion fuel --deuterium-- in a chemical compound in order to either greatly decrease the size of the tankage or to greatly increase the energy density per volume. Not only that, but by storing it in a chemical that is easier to store --less cryogenic, for example-- you also greatly decrease the mass of the tanks.

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I'd like to believe I understood the basics. To decrease volume of ship storage it's essential to compress the reactants. Could there be a way by the 23rd Century to compress deuterium from a liquid into a more solid form or would you need the "chemical compound" (and what would / could this probably be)?

Since it's reasonable to assume Star Fleet engineers could easily realize the possibility of chemical storage of deuterium but choose to store it as a liquid instead, it seems to me, for some technical reason, energy density per kilogram is more important than energy density per liter.

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The "liquid storage" is inspired by publications like the TNG Tech Manual? Would chemical storage have better advantages?

There might be tactical and other considerations that make having a large, ungainly ship undesirable. What kind of difference in volume when heavy hydrogen is stored in a chemical are we talking about?

I had been under the impression (like in "Oblivion") that aliens would harvest deuterium from our sea water but those in "V" apparently could cross vast interstellar distances but didn't have a fracking clue how to manufacture H20... (IIRC we had one Star Trek species with the same "capabilities" but I'll leave it to someone else to name it - Seriously, turned me off at first to continue watching this ST series).

Sorry it's taken so long to respond. I wanted to prepare the table below and make it presentable. This took some time, especially since I made a mistake and had to recalculate everything from scratch. Also my personal life has been rather full of late: teenage daughter drama, 20yr-old daughter drama and girlfriend drama, all feeding of each other.

EmperorTiberius:

There might be tactical and other considerations that make having a large, ungainly ship undesirable. What kind of difference in volume when heavy hydrogen is stored in a chemical are we talking about?

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I've only really studied three chemicals in any detail: heavy water (D2O), duterated methane (CD4) and deuterated propane (C3D8). The largest, most obvious difference is between liquid deuterium and deuterated propane: propane has twice the energy for the same volume but three times LESS energy for the same mass. This is because carbon makes up 2/3s the mass of deuterated propane and contributes nothing to the energy released in all the reactions except the final, most difficult reaction, where the fuel is completely converted to Nickel.

Robert: I will reply to your questions ASAP. As always, you ask interesting questions that require involved answers... Just the way I like 'em! But it takes time to compose those answers. Hopefully, they'll be worth the wait.

I have come to the opinion that the NX-01 used the deuterium-deuterium reaction (DD), 1701 used the Catalyzed-Deuterium reaction (CatDD), 1701-A,B used the Proton-Catalyzed-Deuterium reaction (pCatD), 1701-C,D converted deuterium to carbon (D->C). This is an opinion.

[The energy output of these reactions and their relationship with the fuel is detailed in the table below, though I've not detailed the reactions themselves. If you would like me to detail each reaction, I will. I think I have them all written out somewhere. And if not, figuring them out again shouldn't be hard.]

I also opine that the Romulans used the (DD) until near the end of the Earth-Romulan war, where they engineered (CatDD) reactors, which were still not powerful enough to compete with M/AM; and by the TOS era, they had either (pCatD) or (D->C) reactors powering their ships. By TMP I speculate they used the final reaction calculated here, which converts the whole of the fuel to Nickel. (I notate it as "(*->Ni)" because it is the only reaction that actually burns up *all* the fuel and not just the deuterium within the fuel, which makes this notation more universal in this instance.) I further speculate Romulans stored ultradense deuterium by TMP. Sometime in the TMY era, IMHO, they succeed in building and artificial quantum singularity. (I've got plenty of speculation on this one as well.)

Finally, I speculate that Romulans rely on the interstellar medium more intensely than the Federation does. Some of this speculation can be found in the Let's Talk About the Rom Bop thread linked earlier. I hope to expound on this idea sometime later.

In the mean time, I hope the following table is understandable. Ask about what is not understandable and I'll give a go at explaining.

*Calculations for heavy water do not include burning of the oxygen. This is an oversight for time-saving reasons. (IE, I'm lazy.) This only effects the (*->Ni) reaction calculations. However, the effect is probably large and so this set numbers should not be taken very seriously.
**The assumed wet mass of Enterprise D is 4.96e9 kg. This comes from the TNG:TM. The numbers are similar but smaller if this is the assumed dry mass.

Robert: I will reply to your questions ASAP. As always, you ask interesting questions that require involved answers... Just the way I like 'em! But it takes time to compose those answers. Hopefully, they'll be worth the wait.

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Thanks for the kind words, I don't get a lot of these, lately. But by all means, it can wait if it helps you take care of more pressing issues, first. Sincerely,

This always reminds me of the scene in the original "V-The Visitors" where the main protagonist goes to these huge tanks aboard the V-saucer and opens a valve to taste it. Last time I thought "What is the idiot doing, drinking deuterium?" but of course it just turned out to be water...doh!

I had been under the impression (like in "Oblivion") that aliens would harvest deuterium from our sea water but those in "V" apparently could cross vast interstellar distances but didn't have a fracking clue how to manufacture H20... (IIRC we had one Star Trek species with the same "capabilities" but I'll leave it to someone else to name it - Seriously, turned me off at first to continue watching this ST series).

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Didn't see Oblivion and don't remember V. But I've had the feeling you describe over and over again. SciFi movies and TV series are so often so damned science illiterate. Water is everywhere and races that travel between stars don't need to take over our planet for water. Collecting deuterium would be far easier on Titan than on Earth and there's quite a bit more of it there. Indeed, you can collect deuterium anywhere where there's hydrogen, because it *IS* a kind of hydrogen; and there's hydrogen EVERYWHERE!!

But, on the other hand, it's hard to think of a good reason for star-traveling aliens to come to Earth and take over. Such aliens can make their own, perfect electronic or biological slaves; there's plenty of uninhabited, terraformable planets; resources of all types and kinds are cheap to anyone who can harness enough energy to cross from star to star. The only thing I can think of is xenophobia: destroy the unfamiliar. In which case, we'd be totally screwed. So, for a good story, you have to cling onto something that gives us a chance to survive.

There have been some scifi books that had some good answers: Mote in Gods Eye, Enders Game, Childhoods End, Rama, etc. But these answers are good for the cerebral people who read books, not the glandular movie crowd.

So I have some sympathy for writers and producers who create this tripe, but it so pisses me off none the less!!

I'd like to believe I understood the basics. To decrease volume of ship storage it's essential to compress the reactants. Could there be a way by the 23rd Century to compress deuterium from a liquid into a more solid form or would you need the "chemical compound" (and what would / could this probably be)?

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As it turns out (AFAIK) hydrogen is less dense as a solid than as a liquid, which is also true from water and pig iron. This is an effect of its chemistry (it's electrons) and so is true for both protium and deuterium. (IE light and heavy hydrogen, respectively.) You can, of course, compress liquid hydrogen to greater densities via pressure, but that requires heavier tanks.

Of course, if you apply force fields you can use as much pressure as your field projectors can stand.

There is an answer that might be possible in the 23rd century, or even the late 21st: ultradense deuterium. AFAIK the experiments have not been confirmed yet, but there was an announcement of the discovery of deuterium nuclei sharing electrons much more freely than even metals. It's called the Rydberg state. The stated density was on the order of 130 kg/cc = 130e6 kg/kL. This would be a highly efficient way of storing deuterium fuel. This means a cube a yard on a side would store 13 times the deuterium stored in a Galaxy class! (Assuming Galaxies store D2 as a cryogenic slush at 13K & 1atm, which seems to be the TNG Tech Manual's intent.)

Unfortunately for the Federation, every bit of evidence points to them using slush deuterium as a storage method. Ultra dense deuterium is not hinted at in any of the episodes I remember and none of the books I've read.

The "liquid storage" is inspired by publications like the TNG Tech Manual? Would chemical storage have better advantages?

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Yes. The tech manual specifically states deuterium slush stored at 13 kelvin. It does not state (to my knowledge) the internal pressure or the density, and I don't remember it stating a total mass of fuel; just the volume of the storage tank, the temperature at which the fuel was stored, the word "slush" and a figure for the mass of deuterium lost per unit time. If anyone knows something different, I'd love to be corrected.

I also do not remember any direct statement in any of the episodes. The need for deuterium has come up more then once but I don't remember any direct or implied statement as to the storage method or state of the deuterium. Again, I'd love to be wrong.

This, of course, means my calculations and conclusions are relying on assumptions that are not "cannon". However, I think they were probably the intent of the authors and directors at the time.

Storing deuterium chemically would do only two things for you: make deuterium storage easier and more dense, by volume. Easier because the liquids need not be as cryogenic: 100K instead of 13K (in the case of propane). AgainiIn the case of propane, it's 163% more energy dense per volume. However, this comes at the cost of energy density per kilogram: liquid D2 has 323% more energy per kilogram.

As the above table demonstrates, for rockets, this is an excellent compromise: with the Galaxy class tankage and mass, the worst fusion reaction with propane fuel out performs the best reaction with liquid deuterium fuel. But, apparently, this is not a good compromise for warp ships, even ones that use a fusion rocket for slower than light travel.

I assume there's one or more things I missed or did not understand. Bigger mass always makes bigger power requirements inevitable to move it forward (equally at sublight or FTL), I thought.

I'd be grateful if you could elaborate. Thanks for sharing this with us.

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Ok. I know about rockets, so let's discuss that first. Exhaust velocity and fuel mass is everything for a rocket. Rockets are literally separated into fuel mass and the mass of everything else. Here's why:

If the fuel mass is exactly the same as the mass of everything else in the rocket, and the exhaust velocity is, say, 4000 meters per second, then once all the fuel is burned the rocket's velocity will have changed by 4000 meters per second. If the fuel's exhaust velocity is 2 kps, then the rocket's final velocity will be the same. So higher exhaust velocity means a faster end velocity. The relationship is linear: all else being equal, half the exhaust velocity, half the final rocket velocity. (Unless, of course, you have to take into account relativistic effects.)

However, if the fuel mass is more than the mass of the rest of the rocket, the rocket's end velocity will be more. Conversely, if the ratio is less, then the velocity will be less. But in this case the differences are exponential. Half the ratio is not half the final speed but considerably less. How much less depends on what numbers you started with.

So there's a balancing act: fuels with a better energy densities by mass have higher exhaust velocities because more of their mass has been turned into energy; higher exhaust velocities are more efficient, giving you the same velocity change for less fuel burned. However, fuels of higher density make for a better fuel-to-rocket mass ratio, which can overcome the disadvantage of a lower exhaust velocity.

This is exactly the case for the deuterium/propane comparison. For the same tankage and vehicle, you get a much better mass ratio for propane than liquid deuterium and, even though it releases much less energy when it burns, you get a far superior rocket performance.

However, my argument here is that this can not be true for a warp ship or they would use chemically stored deuterium instead of storing it as a liquid. But, according to everything I think I know, this is not the case.

Of course, I'm assuming quite a bit to make this conclusion, so it's shakey at best. The "real" explanation is that the writers didn't think of it. But the in-universe explanation must be (IMHO) that the per-mass energy-density is more important than the per-volume energy-density. Which is another way of saying extra mass penalizes warp drive more than extra volume.

I especially like where you put the hydrogen collectors. I think that makes much more sense than in the nacelles, like TNG. I've downloaded the image to my machine and will use it as reference if I ever need to. Damn fine work.

I just from this site that slush hydrogen is approximately "0.1967 gram per cubic centimetre". This is equivalent to 196.7 kg/kL, which is the units I used in the above table, in which I calculated for 165.6 kg/kL at 20K: liquid, not slush.

The thing that gets me, though, is that when I went looking for data before (about two years ago, so I forgot where I got the data) I found that it was 152 kg/kL as a solid, less than what I was quoting as a liquid.

Thus my earlier "deuterium is less dense as a solid" comment earlier.

At the same time, I've encounter the 196.7 kg/kL data point recently but I didn't give it much credence.

....
I also want to state that my statements about rocket propulsion is a bit glib. Exhaust velocity does not effect rocket velocity linearly. The effects are also logarithmic. But describing the difference in the curves is not easy for me to describe. As such, sometimes it's better to have a better exhaust velocity than it is to have a high mass ratio. It just depends.

I especially like where you put the hydrogen collectors. I think that makes much more sense than in the nacelles, like TNG. I've downloaded the image to my machine and will use it as reference if I ever need to.

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Thank you very much. A year ago I started this thread - http://www.trekbbs.com/showthread.php?t=199522 - regarding the possibly intended function of the rotating nacelle caps of the TOS Enterprise, hope you find some of the observations interesting (I just consider this thread dormant).

Supposedly the TOS Enterprise took in "space matter" and "space energy" (dark energy???), the Official TMP Blueprints specified such intakes for the refit Enterprise.

Bob

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Anymore, I've decided that the original Enterprise used something even more exotic than the types of matter-antimatter described in TNG and beyond. Particularly in light of how energetic the explosion was in "Obsession".

That they called it simply "antimatter" I attribute to a colloquialism, similar to how pilots today call their jet fuel "gas".

^^ That's quite a can worm opener you brought along and a delicate subject.

Indeed, if I'm supposed to take it literally that our Kirk visited an antimatter universe in "The Alternative Factor" or that dilithium crystals (matter) are supposedly immune to antimatter, I'd rather assume "antimatter" to be some form of colloquialism as you just suggested.

On the other hand it's pretty much spoken out, that matter-antimatter annihilation somehow propels the Enterprise.

The question would remain what kind of colloquialism "matter" would stand for.

I'd assume it's some kind of normal matter, but it seems inefficient to use hydrogen isotopes, when there are more dense materials that could be used. Or perhaps it's a dark matter/energy type of reaction as you alluded to above.

It's also worth mentioning that no matter how dire the power situation was in the original series, there never seemed to be concerns about the reactors or their reactants exploding for some reason (later to be the ubiquitous "warp core breach" in later shows), indicating that the power systems were much more robust and the reactants perhaps more stable.